BPS Wilson loops and quiver varieties

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15 Citations (Scopus)


Three dimensional supersymmetric field theories have large moduli spaces of circular Wilson loops preserving a fixed set of supercharges. We simplify previous constructions of such Wilson loops and amend and clarify their classification. For a generic quiver gauge theory we identify the moduli space as a quotient of for some m by an appropriate symmetry group. These spaces are quiver varieties associated to a cover of the original quiver or a subquiver thereof. This moduli space is generically singular and at the singularities there are large degeneracies of operators which seem different, but whose expectation values and correlation functions with all other gauge invariant operators are identical. The formulation presented here, where the Wilson loops are on S 3 or squashed S3b also allows to directly implement a localization procedure on these observables, which previously required an indirect cohomological equivalence argument.

Original languageEnglish
Article number385402
JournalJournal Of Physics A-Mathematical And Theoretical
Issue number38
Publication statusPublished - 25 Sept 2020


  • 3D theories
  • Wilson loops
  • moduli spaces
  • supersymmetry


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